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1 Ungar, Abraham A Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession I11260 2001 eBook  
2 Ungar, A.A Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession I10899 2002 eBook  
3 Duplij, S Concise Encyclopedia of Supersymmetry I10524 2004 eBook  
4 Doktorov, Evgeny V A Dressing Method in Mathematical Physics I05617 2007 eBook  
5 Borowiec, Andrzej Spinors, Twistors, Clifford Algebras and Quantum Deformations I05350 1993 eBook  
6 Van Oystaeyen, Freddy Methods in Ring Theory I04623 1984 eBook  
7 Tanner, Elizabeth A Noncompact Lie Groups and Some of Their Applications I04271 1994 eBook  
8 Ibort, Alberto Integrable Systems, Quantum Groups, and Quantum Field Theories I03653 1993 eBook  
9 Dlab, V Finite Dimensional Algebras and Related Topics I02890 1994 eBook  
10 Carter, R.W Algebraic Groups and their Representations I02777 1998 eBook  
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TitleBeyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces
Author(s)Ungar, Abraham A
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2001.
DescriptionXLII, 419 p. 25 illus : online resource
Abstract Note"I cannot define coincidence [in mathematics]. But 1 shall argue that coincidence can always be elevated or organized into a superstructure which perfonns a unification along the coincidental elements. The existence of a coincidence is strong evidence for the existence of a covering theory. " -Philip 1. Davis [Dav81] Alluding to the Thomas gyration, this book presents the Theory of gy?? rogroups and gyrovector spaces, taking the reader to the immensity of hyper?? bolic geometry that lies beyond the Einstein special theory of relativity. Soon after its introduction by Einstein in 1905 [Ein05], special relativity theory (as named by Einstein ten years later) became overshadowed by the ap?? pearance of general relativity. Subsequently, the exposition of special relativity followed the lines laid down by Minkowski, in which the role of hyperbolic ge?? ometry is not emphasized. This can doubtlessly be explained by the strangeness and unfamiliarity of hyperbolic geometry [Bar98]. The aim of this book is to reverse the trend of neglecting the role of hy?? perbolic geometry in the special theory of relativity, initiated by Minkowski, by emphasizing the central role that hyperbolic geometry plays in the theory
ISBN,Price9789401091220
Keyword(s)1. Astronomy, Observations and Techniques 2. Astronomy???Observations 3. EBOOK 4. EBOOK - SPRINGER 5. MATHEMATICAL PHYSICS 6. Non-associative Rings and Algebras 7. Nonassociative rings 8. Observations, Astronomical 9. Rings (Algebra) 10. Theoretical, Mathematical and Computational Physics
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TitleBeyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces
Author(s)Ungar, A.A
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2002.
Description464 p : online resource
Abstract NoteEvidence that Einstein's addition is regulated by the Thomas precession has come to light, turning the notorious Thomas precession, previously considered the ugly duckling of special relativity theory, into the beautiful swan of gyrogroup and gyrovector space theory, where it has been extended by abstraction into an automorphism generator, called the Thomas gyration. The Thomas gyration, in turn, allows the introduction of vectors into hyperbolic geometry, where they are called gyrovectors, in such a way that Einstein's velocity additions turns out to be a gyrovector addition. Einstein's addition thus becomes a gyrocommutative, gyroassociative gyrogroup operation in the same way that ordinary vector addition is a commutative, associative group operation. Some gyrogroups of gyrovectors admit scalar multiplication, giving rise to gyrovector spaces in the same way that some groups of vectors that admit scalar multiplication give rise to vector spaces. Furthermore, gyrovector spaces form the setting for hyperbolic geometry in the same way that vector spaces form the setting for Euclidean geometry. In particular, the gyrovector space with gyrovector addition given by Einstein's (M??bius') addition forms the setting for the Beltrami (Poincar??) ball model of hyperbolic geometry. The gyrogroup-theoretic techniques developed in this book for use in relativity physics and in hyperbolic geometry allow one to solve old and new important problems in relativity physics. A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein
ISBN,Price9780306471346
Keyword(s)1. Astronomy, Observations and Techniques 2. Astronomy???Observations 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY 6. MATHEMATICAL PHYSICS 7. Non-associative Rings and Algebras 8. Nonassociative rings 9. Observations, Astronomical 10. Rings (Algebra) 11. Theoretical, Mathematical and Computational Physics
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TitleConcise Encyclopedia of Supersymmetry : And Noncommutative Structures in Mathematics and Physics
Author(s)Duplij, S
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2004.
DescriptioneReference : online resource
Abstract NoteThe book is the first full-size Encyclopedia which simultaneously covers such well-established and modern subjects as quantum field theory, supersymmetry, supergravity, M-theory, black holes and quantum gravity, noncommutative geometry, representation theory, categories and quantum groups, and their generalizations. The extraordinary historical part "the SUSY story," more than 700 authored articles from more than 250 high-level experts (including Nobel Prize Winner Gerard 't Hooft), a detailed (50 pages) Subject/Article three level index and an Author index, make the SUSY Encyclopedia an outstanding and indispensable book on the desk of researchers, experts, Ph.D. students, specialists and professionals in modern methods of theoretical and mathematical physics
ISBN,Price9781402045226
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. MATHEMATICAL PHYSICS 6. Non-associative Rings and Algebras 7. Nonassociative rings 8. Rings (Algebra) 9. Theoretical, Mathematical and Computational Physics
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TitleA Dressing Method in Mathematical Physics
Author(s)Doktorov, Evgeny V;Leble, Sergey B
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2007.
DescriptionXXIV, 383 p : online resource
Abstract NoteThe monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation. The Moutard and Darboux transformations discovered in XIX century as applied to linear equations, the B??cklund transformation in differential geometry of surfaces, the factorization method, the Riemann-Hilbert problem in the form proposed by Shabat and Zakharov for soliton equations and its extension in terms of the d-bar formalism comprise the main objects of the book. Throughout the text, a generally sufficient "linear experience" of readers is exploited, with a special attention to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions. Various linear equations of classical and quantum mechanics are solved by the Darboux and factorization methods. An extension of the classical Darboux transformations to nonlinear equations in 1+1 and 2+1 dimensions, as well as its factorization are discussed in detail. The applicability of the local and non-local Riemann-Hilbert problem-based approach and its generalization in terms of the d-bar method are illustrated on various nonlinear equations
ISBN,Price9781402061400
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. CLASSICAL ELECTRODYNAMICS 4. EBOOK 5. EBOOK - SPRINGER 6. ELECTRODYNAMICS 7. ENGINEERING MATHEMATICS 8. Functions of a Complex Variable 9. FUNCTIONS OF COMPLEX VARIABLES 10. Mathematical and Computational Engineering 11. Mathematical Methods in Physics 12. Non-associative Rings and Algebras 13. Nonassociative rings 14. OPTICS 15. PHYSICS 16. Rings (Algebra)
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TitleSpinors, Twistors, Clifford Algebras and Quantum Deformations : Proceedings of the Second Max Born Symposium held near Wroc??aw, Poland, September 1992
Author(s)Borowiec, Andrzej;Jancewicz, Bernard;Oziewicz, Zbigniew
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXXV, 430 p : online resource
Abstract NoteZBIGNIEW OZIEWICZ University of Wroclaw, Poland December 1992 The First Max Born Symposium in Theoretical and Mathematical Phy?? sics, organized by the University of Wrodaw, was held in September 1991 with the intent that it would become an annual event. It is the outgrowth of the annual Seminars organized jointly since 1972 with the University of Leipzig. The name of the Symposia was proposed by Professor Jan Lopu?? szanski. Max Born, an outstanding German theoretical physicist, was born in 1883 in Breslau (the German name of Wrodaw) and educated here. The Second Max Born Symposium was held during the four days 24- 27 September 1992 in an old Sobotka Castle 30 km west of Wrodaw. The Sobotka Castle was built in the eleventh century. The dates engraved on the walls of the Castle are 1024, 1140, and at the last rebuilding, 1885. The castle served as a cloister until the end of the sixteenth century
ISBN,Price9789401117197
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. MATHEMATICAL PHYSICS 4. Non-associative Rings and Algebras 5. Nonassociative rings 6. Rings (Algebra) 7. Theoretical, Mathematical and Computational Physics
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TitleMethods in Ring Theory
Author(s)Van Oystaeyen, Freddy
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1984.
DescriptionVIII, 576 p : online resource
ISBN,Price9789400963696
Keyword(s)1. ALGEBRA 2. Associative rings 3. Associative Rings and Algebras 4. EBOOK 5. EBOOK - SPRINGER 6. Non-associative Rings and Algebras 7. Nonassociative rings 8. Rings (Algebra)
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TitleNoncompact Lie Groups and Some of Their Applications
Author(s)Tanner, Elizabeth A;Wilson, R
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1994.
Description512 p : online resource
Abstract NoteDuring the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig?? nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy?? namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr
ISBN,Price9789401110785
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. GROUP THEORY 6. Group Theory and Generalizations 7. LIE GROUPS 8. Manifolds (Mathematics) 9. MATHEMATICAL PHYSICS 10. Non-associative Rings and Algebras 11. Nonassociative rings 12. Rings (Algebra) 13. Theoretical, Mathematical and Computational Physics 14. TOPOLOGICAL GROUPS 15. Topological Groups, Lie Groups
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TitleIntegrable Systems, Quantum Groups, and Quantum Field Theories
Author(s)Ibort, Alberto;Rodr??guez, M.A
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXI, 502 p : online resource
Abstract NoteIn many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects
ISBN,Price9789401119801
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. LIE GROUPS 4. MATHEMATICAL PHYSICS 5. Non-associative Rings and Algebras 6. Nonassociative rings 7. PARTIAL DIFFERENTIAL EQUATIONS 8. Rings (Algebra) 9. Theoretical, Mathematical and Computational Physics 10. TOPOLOGICAL GROUPS 11. Topological Groups, Lie Groups
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TitleFinite Dimensional Algebras and Related Topics
Author(s)Dlab, V;Scott, Leonard
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1994.
DescriptionXIV, 392 p : online resource
Abstract NoteBased on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance
ISBN,Price9789401715560
Keyword(s)1. ALGEBRA 2. COMMUTATIVE ALGEBRA 3. Commutative rings 4. Commutative Rings and Algebras 5. EBOOK 6. EBOOK - SPRINGER 7. Non-associative Rings and Algebras 8. Nonassociative rings 9. Rings (Algebra)
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TitleAlgebraic Groups and their Representations
Author(s)Carter, R.W;Saxl, J
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1998.
DescriptionXVIII, 374 p : online resource
Abstract NoteThis volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al?? gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet?? ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups
ISBN,Price9789401153089
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. LIE GROUPS 6. Non-associative Rings and Algebras 7. Nonassociative rings 8. Rings (Algebra) 9. TOPOLOGICAL GROUPS 10. Topological Groups, Lie Groups
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